In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems’ transitions across phases, (universal) critical exponents, and related dynamical properties. Here we consider the functionality of systems, notably operations in socio-technical ones, production in economic ones and possibly information-processing in biological ones, where timing is of crucial importance. We introduce a stylized model on temporal networks with the magnitude of delay-mitigating buffers as the control parameter. The model exhibits temporal criticality, a novel form of critical behavior in time. We characterize fluctuations near criticality, commonly referred to as “avalanches”, and identify the corresponding critical exponents. We show that real-world temporal networks, too, exhibit temporal criticality. We also explore potential connections with the Mode-Coupling Theory of glasses and the directed polymer problem.


Moran, J., Romeijnders, M., Le Doussal, P., Pijpers, F.P., Weitzel, U., Panja, D. & Bouchaud, J-P. (2023). Temporal criticality. INEt Oxford Working Paper No. 2023-18.
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